arXiv subjects

Gordan Zitkovic

Publications and source records attributed to Gordan Zitkovic.

25 records · Page 2Linked to original sources

arXiv2007

On the semimartingale property via bounded logarithmic utility

This paper provides a new version of the condition of Di Nunno et al. (2003), Ankirchner and Imkeller (2005) and Biagini and \{O}ksendal (2005) ensuring the semimartingale property for a large class of continuous stochastic processes. Unlike our predecessors, we base our modeling framework on the concept of portfolio proportions which yields a short self-contained proof of the main theorem, as well as a counterexample, showing that analogues of our results do not hold in the discontinuous setting.

q-fin.PM↗

arXiv2007

Stability of utility-maximization in incomplete markets

The effectiveness of utility-maximization techniques for portfolio management relies on our ability to estimate correctly the parameters of the dynamics of the underlying financial assets. In the setting of complete or incomplete financial markets, we investigate whether small perturbations of the market coefficient processes lead to small changes in the agent's optimal behavior derived from the solution of the related utility-maximization problems. Specifically, we identify the topologies on the parameter process space and the solution space under which utility-maximization is a continuous operation, and we provide a counterexample showing that our results are best possible, in a certain sense. A novel result about the structure of the solution of the utility-maximization problem where prices are modeled by continuous semimartingales is established as an offshoot of the proof of our central theorem.

q-fin.PM↗

arXiv2007

Maximizing the Growth Rate under Risk Constraints

We investigate the ergodic problem of growth-rate maximization under a class of risk constraints in the context of incomplete, Itô-process models of financial markets with random ergodic coefficients. Including {\em value-at-risk} (VaR), {\em tail-value-at-risk} (TVaR), and {\em limited expected loss} (LEL), these constraints can be both wealth-dependent(relative) and wealth-independent (absolute). The optimal policy is shown to exist in an appropriate admissibility class, and can be obtained explicitly by uniform, state-dependent scaling down of the unconstrained (Merton) optimal portfolio. This implies that the risk-constrained wealth-growth optimizer locally behaves like a CRRA-investor, with the relative risk-aversion coefficient depending on the current values of the market coefficients.

q-fin.PM↗

arXiv2007

Optimal consumption from investment and random endowment in incomplete semimartingale markets

We consider the problem of maximizing expected utility from consumption in a constrained incomplete semimartingale market with a random endowment process, and establish a general existence and uniqueness result using techniques from convex duality. The notion of asymptotic elasticity of Kramkov and Schachermayer is extended to the time-dependent case. By imposing no smoothness requirements on the utility function in the temporal argument, we can treat both pure consumption and combined consumption/terminal wealth problems, in a common framework. To make the duality approach possible, we provide a detailed characterization of the enlarged dual domain which is reminiscent of the enlargement of $L^1$ to its topological bidual $(L^{\infty})^*$, a space of finitely-additive measures. As an application, we treat the case of a constrained It\^ o-process market-model.

q-fin.PM↗

arXiv2007

A filtered version of the bipolar theorem of Brannath and Schachermayer

We extend the Bipolar Theorem of Brannath and Schachermayer (1999) to the space of nonnegative cadlag supermartingales on a filtered probability space. We formulate the notion of fork-convexity as an analogue to convexity in this setting. As an intermediate step in the proof of our main result we establish a conditional version of the Bipolar theorem. In an application to mathematical finance we describe the structure of the set of dual processes of the utility maximization problem of Kramkov and Schachermayer (1999) and give a budget-constraint characterization of admissible consumption processes in an incomplete semimartingale market.

math.PR↗

arXiv2007

Utility Maximization with a Stochastic Clock and an Unbounded Random Endowment

We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and uniqueness for a large class of utility maximization problems including the classical ones of terminal wealth or consumption, as well as the problems depending on a random time-horizon or multiple consumption instances. As an example we treat explicitly the problem of maximizing the logarithmic utility of a consumption stream, where the local time of an Ornstein-Uhlenbeck process acts as a stochastic clock.

q-fin.GN↗

arXiv2005

Utility Maximization with a Stochastic Clock and an Unbounded Random Endowment

We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and uniqueness for a large class of utility-maximization problems including the classical ones of terminal wealth or consumption, as well as the problems that depend on a random time horizon or multiple consumption instances. As an example we explicitly treat the problem of maximizing the logarithmic utility of a consumption stream, where the local time of an Ornstein-Uhlenbeck process acts as a stochastic clock.

math.PR↗